Abstract
Many applications, manipulation or just visualization of discrete volumes are time consuming problems. The general idea to solve these difficulties is to transform, in a reversible way, those volumes into Euclidean polyhedra. A first step of this process consists in a Digital Plane Segmentation of the discrete object’s surface. In this paper, we present an algorithm to construct an optimal, in the number of vertices, discrete volume polyhedral representation (i.e. vertices and faces adjacencies).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ph. Borianne and J. Françon. Reversible polyhedrization of discrete volumes. In DGCI’94, pages 157–168, Grenoble, France, sept. 1994.
L. Buzer. An incremental linear time algorithm for digital line and plane recognition using a linear incremental feasibility problem. In A. Braquelaire, J.-O. Lachaud, and A. Vialard, editors, DGCI’02, volume 2301 of Lect. Notes of Comp. Sci., pages 372–381. Springer Verlag, 2002.
J.M. Chassery, F. Dupont, I. Sivignon, and J. Vittone. Recognition of digital naive planes. In ICIAP’01 11th International Conference on Image Analysis and Processing, pages 662–636, September 2001.
I. Debled-Rennesson and J.-P. Reveillès. An incremental algorithm for digital plane recognition. In DGCI’94, pages 207–222, September 1994.
J. Françon, J. M. Schramm, and M. Tajine. Recognizing arithmetic straight lines and planes. In S. Miguet A. Montanvert and S. Ubéda, editors, DGCI’96, volume 1176 of Lect. Notes of Comp. Sci., pages 141–150. Springer Verlag, 1996.
D. S. Hochbaum, editor. Approximation algorithms for NP-hard problems. PWS Publishing Company, 1997.
C.E. Kim and A. Rosenfeld. Convex digital solids. IEEE Trans. on Pattern Anal. Machine Intell., PAMI-4(6):612–618, 1982.
C.E. Kim and I. Stojmenović. On the recognition of digital planes in three dimensionnal space. Pattern Recognition Letters, 32:612–618, 1991.
R. Klette. Digital Geometry-The birth of a new discipline, chapter 1. 2001. Retirement of A. Rosenfeld.
R. Klette and H. J. Sun. Digital planar segment based polyhedrization for surface area estimation. In C. Arcelli, L.P. Cordella, and G. Sanniti di Baja, editors, International Workshop on Visual Form 4, volume 2059 of Lect. Notes Comput. Sci., pages 356–366. Springer-Verlag, 2001.
L. Papier and J. Françon. Polyhedrization of the boundary of a voxel object. In M. Couprie G. Bertrand and L. Perroton, editors, DGCI’99, volume 1568 of Lect. Notes of Comp. Sci., pages 425–434. Springer Verlag, 1999.
J.-P. Reveillès. Géométrie discréte, calcul en nombres entiers et algorithmique. PhD thesis, Université Louis Pasteur, 1991.
Carsten Thomassen. On the complexity of finding a minimum cycle cover of a graph. SIAM Journal on Computing, 26(3):675–677, June 1997.
P. Veelaert. Digital planarity of rectangular surface segments. IEEE Trans. Pattern Anal. Machine Intell., PAMI-16:647–653, 1994.
P. Veelaert. Concurrency of line segments in uncertain geometry. In A. Braquelaire, J.-O. Lachaud, and A. Vialard, editors, DGCI’02, volume 2301 of Lect. Notes of Comp. Sci., pages 289–300. Springer Verlag, April 2002.
Joëlle Vittone. Caractérisation et reconnaissance de droites et de plans en géométrie discrète. PhD thesis, Université Joseph Fourier, Grenoble, France, 1999.
D. B. West. Introduction to Graph Theory. Prentice Hall, 2 edition, 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sivignon, I., Coeurjolly, D. (2003). From Digital Plane Segmentation to Polyhedral Representation. In: Asano, T., Klette, R., Ronse, C. (eds) Geometry, Morphology, and Computational Imaging. Lecture Notes in Computer Science, vol 2616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36586-9_23
Download citation
DOI: https://doi.org/10.1007/3-540-36586-9_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00916-0
Online ISBN: 978-3-540-36586-0
eBook Packages: Springer Book Archive